Giving them direct access to the data and analytical tools reminds me of a story Bill Cosby told a century or so ago, about his mother wanting to drive his Shelby Cobra. As I recall it, his mother got behind the wheel, revved the engine, let out the clutch, and approximately a tenth of a second later found herself several blocks away. At that point, she screeched to a stop, turned off the engine, ambled back to Cosby, handed him the keys, and without saying a word, walked away.
Changing metaphors, if your company's BI toolkit is a Shelby Cobra, company decision makers will, for the most part, be passengers. Your analysts and statisticians are the drivers.
There are plenty of ways to mess up statistical analyses so that they deliver the wrong answer, especially when using data not originally collected for the purpose of supporting the analyses you're conducting. Without professionals handling the tricky parts, having analytics will be worse than guessing because they'll give you authoritative-looking but potentially very wrong answers.
Data analytics criterion No. 2: Evidence-based decision making
The best analytics in the world have no value if nobody uses them to make decisions. That being the case, before spending time, money, and effort on analytics capabilities, take a hard look at your company's decision makers.
If they're the sorts of folks who say, in a frustrated tone of voice, "How can we make this decision? We need data!" then get ready to rock 'n' roll. But if they're the sort who instead say, "Here's what we're going to do. My gut tells me it's the right answer," all of your other priorities -- including your ballroom dancing lessons -- are more important than the analytics improvement project.
Data analytics criterion No. 3: Culture of honest inquiry
Without a culture of honest inquiry, the executives who prefer data-driven decision making are probably searching for ammunition, not for answers to questions. That is, they're likely to start with the answer they want and solve for the analysis that supports it.
It's a more sophisticated form of trusting one's gut, but in the end, that's all it is.
Getting started: Small team, adequate resources, full agile ahead
If your company has strong statisticians and analysts, executives who want evidence to support decision making, and a culture of honest inquiry, then it's time to start building. The question now is how to go about it.
The answer: This isn't the time to forget everything we ever learned about the advantages of agile over waterfall methodologies.
The best approach I know of for getting started is to pair up one of your best data analysts with one of your best statistical analysts, and get them together with the most gung-ho evidence-driven decision maker in the company. Be sure to set them up with their own virtual server, DBMS instance, and data access rights so that they don't have to beg for computing resources -- then turn them loose.